Impossibility of the Cylindrically Symmetric Einstein-Straus Model

Abstract

The classical Einstein-Straus problem treats the influence of the expansion of the universe on the static vacuum surrounding a spherically symmetric object. In this Letter we study the next simplest step by dropping the assumption of spherical symmetry and considering the case of cylindrical symmetry. Our main result is that the cylindrically symmetric analog of the Einstein-Straus model is impossible, even without any restriction on the matter content of the static cavity. This fact forbids the embedding of some static objects (say strings or similar objects) into the standard cosmological models.